Question

The data below are the monthly average high temperatures for New York City. What is the five-number summary? 40, 40, 48, 61, 72, 78, 84, 84, 76, 65, 54, 42
Select the correct answer below:
A) Sample minimum: 42, Sample maximum: 78
Q1: 45, Median: 63, Q3: 77
B) Sample minimum: 40, Sample maximum: 84
Q1: 45, Median: 63, Q3: 77
C) Sample minimum: 40, Sample maximum: 42
Q1: 54.5, Median: 81, Q3: 70.5
D) Sample minimum: 40, Sample maximum: 84
Q1: 40, Median: 61, Q3: 76

Answer 1

Answer:

B) Sample minimum: 40, Sample maximum: 84

Q1: 45, Median: 63, Q3: 77

Step-by-step explanation:

The first step is to write the temperatures in crescent order:

40, 40, 42, 48, 54, 61, 65, 72, 76, 78, 84, 84,

The sample minimum is the lowest value = 40

The sample maximum is the highest value = 84.

Since there are 12 numbers, the sample median is the average between the 6th and 7th terms:

$M = \frac{61+65}{2}\\ M=63$

The first quartile is the average between the 3rd and 4th terms:

$Q_1 = \frac{42+48}{2}\\ Q_1=45$

The third quartile is the average between the 9th and 10th terms:

$Q_3 = \frac{76+78}{2}\\ Q_3=77$

Therefore, the answer is:

B) Sample minimum: 40, Sample maximum: 84

Q1: 45, Median: 63, Q3: 77